Related papers: Orderly divergence of Levy Gamma integrals
Discrete normal distributions are defined as the distributions with prescribed means and covariance matrices which maximize entropy on the integer lattice support. The set of discrete normal distributions form an exponential family with…
We study a discrete-to-continuous Gamma-limit of a family of high-contrast double porosity type functionals defined on a scaled integer lattice. Under periodicity and p-growth conditions we prove the homogenization result and describe the…
Fractional derivatives are a well-studied generalization of integer order derivatives. Naturally, for optimization, it is of interest to understand the convergence properties of gradient descent using fractional derivatives. Convergence…
In this paper we consider the rate of convergence of solutions of a scalar ordinary differential equation which is a perturbed version of an autonomous equation with a globally stable equilibrium. Under weak assumptions on the nonlinear…
In the present paper we shall study a variational problem relating the weighted Hardy inequalities with sharp missing terms. As weights we treat non-doubling functions of the distance to the boundary of bounded domain.
We propose a new family of regularized R\'enyi divergences parametrized not only by the order $\alpha$ but also by a variational function space. These new objects are defined by taking the infimal convolution of the standard R\'enyi…
In some inferential statistical methods, such as tests and confidence intervals, it is important to describe the stochastic behavior of statistical functionals, aside from their large sample properties. We study such behavior in terms of…
A gauge invariant partition function is defined for gauge theories which leads to the standard quantization. It is shown that the descent equations and consequently the consistent anomalies and Schwinger terms can be extracted from this…
A moderate deviation principle for nonlinear functions of Gaussian processes is established. The nonlinear functions need not be locally bounded. Especially, the logarithm is allowed. (Thus, small deviations of the process are relevant.)…
Distributed order fractional Langevin-like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent. It is shown that these fractional Langevin equations of distributed order can be…
Let $(\xi,\eta)$ be a bivariate L\'evy process such that the integral $\int\_0^\infty e^{-\xi\_{t-}} d\eta\_t$ converges almost surely. We characterise, in terms of their \LL measures, those L\'evy processes for which (the distribution of)…
The Lagrange problem is established in the discrete field theory subject to constraints with values in a Lie group. For the admissible sections that satisfy a certain regularity condition, we prove that the critical sections of such…
We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…
For a general free L\'evy process, we prove the existence of its higher variation processes as limits in distribution, and identify the limits in terms of the L\'evy-It\^o representation of the original process. For a general free compound…
We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool…
In this paper we consider convergence of moments in the small-time limit theorems for L\'evy processes. We provide precise asymptotics for all the absolute moments of positive order. The convergence of moments in limit theorems holds…
We show that if a nontrivial group admits a locally invariant ordering, then it admits uncountably many locally invariant orderings. For the case of a left-orderable group, we provide an explicit construction of uncountable families of…
We prove some invariance principles for processes which generalize FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution. The limiting processes are extensions of the fractional L\'evy…
In this paper, we study some aspects on random analysis on the L\'eevy stochastic processes with margins following generalized hyperbolic distributions generated by gamma laws. In particular we study the boundedness of its total variations…
Stochastic modelling necessitates an interpretation of noise. In this paper, we describe the loss of deterministically stable behaviour in a fundamental fluid mechanics problem, conditional to whether noise is introduced in the sense of…